Has anyone considered what the dynamic pressure might be like in the cockpit with the door closed and one or more windshield panels missing.

Air flow past the missing panel might result in a lowering of pressure inside the cockpit (ref venturi / Bernoulli) OR there could be some ram effect.

I can well imagine that the environment would be extremely turbulent and debilitating (deadly) but not so sure that you'd be in a low pressure environment or that O2 partial pressure would be a problem in itself.

According to ISA static pressure is .228 Bar. Density 0.35 kg/m3. Speed =400 kts = +/- 200m/s (ignoring wind speed) Dynamic pressure at stagnation point is thus 0.5*0.35*200^2=0.07 Bar, thus about a third outside pressure making the total pressure in the cockpit .3 Bar, equivalent to 30k altitude (at best).

The static pressure with a side window would be the static outside air pressure, as the dynamic pressure is caused by the airplane speed, not a narrowing of a channel.

Another issue would be the deafening noise inside the cockpit flying at 400 knots TAS with an open window...